Quasi-de Sitter Expansion Research Articles

Generalized non-local R2-like inflation

The R2 inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d’Alembertian operator. In this paper, we derive a most general theory of gravity admitting R2 inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local R2-like inflation and obtain the scalar spectral index ns ≈ 1 − frac{2}{N} and any value of the tensor-to-scalar ratio r < 0.036. In this theory, tensor spectral index can be either positive or negative nt ≶ 0 and the well-known consistency relation r = –8nt is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local R2-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

Dynamical analysis of the Tsallis holographic dark energy models with event horizon as cut-off and interaction with matter

The model of generalized Tsallis holographic dark energy (which is known to be particular representative of Nojiri–Odintsov HDE) with event horizon as cut-off is investigated using methods of dynamical analysis. We take into consideration possible interaction with dark energy and matter in various forms. Critical points are determined. Cosmological evolution of the universe depends from interaction parameters. If we use event horizon scale as cut-off quasi-de Sitter expansion is possible only for interaction of type [Formula: see text] (where [Formula: see text] is the Hubble parameter). For interactions [Formula: see text] and [Formula: see text] universe eventually stops ([Formula: see text]) or ends its existence in final singularity ([Formula: see text]). In the first case, fraction of dark energy tends to [Formula: see text] or constant value lesser than 1 because dynamical equilibrium between matter and dark energy is established on late times.

Analytic approach to non-slow-roll inflation

Brief periods of non-slow-roll evolution during inflation can produce interesting observable consequences, as primordial black holes, or an inflationary gravitational wave spectrum enhanced at small scales. We develop a model independent, analytic approach for studying the predictions of single-field scenarios which include short phases of slow-roll violation. Our method is based on Taylor expanding the equations for cosmological fluctuations in a small quantity, which parameterizes the duration of the non-slow-roll eras. The super-horizon spectrum of perturbations is described by few effective parameters, and is characterized by a pronounced dip followed by a rapid growth in its amplitude, as typically found in numerical and analytical studies. The dip position $k_{\rm dip}/k_*$ and the maximal enhancement $\Pi_{\rm max}$ of the spectrum towards small scales are found to be related by the law $k_{\rm dip}/k_*\propto \Pi_{\rm max}^{-1/4}$, and we determine the proportionality constant. For a single epoch of slow-roll violation we confirm previous studies, finding that the steepest slope of the spectrum well after the dip has spectral index $n-1\,=\,4$. On the other hand, with multiple phases of slow-roll violation, the slope of the spectrum is generally enhanced. For example, when two epochs of slow-roll violation take place, separated by a phase of quasi-de Sitter expansion, we find that the spectral index can reach the value $n-1\,=\,8$. This phenomenon indicates that the slope of the spectrum keeps memory of the history of non-slow-roll phases occurred during inflation.

Galileon inflation field with three dark eras of the universe

In this paper, we discuss possible three early eras of the universe in the theoretical context of the Galilean cosmology. The first phase is a slow-roll inflation phase in which the friction term in the equations of motion dominates over the kinetic term. This is the initial vacuum state leading to quasi-de Sitter expansion. The second phase is where the cosmological perturbations are supposed to be generated. In this phase, the friction term is supposed to be negligible which leads to the appearance of the Galileon inflation field. The third phase is the reheating phase in the standard cosmology, where the oscillations of a canonical scalar field in the model lead to this phase. These three eras for the early universe are shown by a single master equation of the theory. However, we compute observational indices (the scalar spectral index parameter and the tensor-to-scalar ratio) for the era where the era that the perturbations are produced. Finally, we compare viability of the theoretical findings with the latest Planck observational data.

Production and backreaction of spin-2 particles of SU(2) gauge field during inflation

Primordial SU(2) gauge fields with an isotropic background lead to the production of spin-2 particles during inflation. We provide a unified formalism to compute this effect in all of the inflation models with isotropic SU(2) gauge fields such as Gauge-flation and Chromo-Natural inflation with and without spectator axion fields or the mass of the gauge field from the Higgs mechanism. First, we calculate the number and energy densities of the spin-2 particles. We then obtain exact analytical formulae for their backreaction on the background equations of motion of SU(2) and axion fields in (quasi) de Sitter expansion, which were calculated only numerically for one particular model in the literature. We show that the backreaction is directly related to the number density of the spin-2 field. Second, we relate the number density of the spin-2 particles to the power spectrum and the energy density of the gravitational waves sourced by them. Finally, we use the size of the backreaction to constrain the parameter space of the models. We find that the tensor-to-scalar ratio of the sourced gravitational waves can at most be on the order of that of the vacuum contribution to avoid a large backreaction on slow-roll dynamics of the gauge ssand axion fields in quasi-de Sitter expansion.

Inflation driven by massive vector fields with derivative self-interactions

Inspired by the Generalized Proca Theory, we study a vector–tensor model of inflation with massive vector fields and derivative self-interactions. The action under consideration contains a usual Maxwell-like kinetic term, a general potential term and a term with nonminimal derivative coupling between the vector field and gravity, via the dual Riemann tensor. In this theory, the last term contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling. In this scenario, taking into account a spatially flat Friedmann–Robertson–Walker (FRW) universe and a general vector field, we obtain the general expressions for the equation of motion and the total energy–momentum tensor. Choosing a Proca-type potential, a suitable inflationary regimen driven by massive vector fields is studied. In this model, the isotropy of expansion is guaranteed by considering a triplet of orthogonal vector fields. In order to obtain an inflationary solution with this model, the quasi de Sitter expansion was considered. In this case, the vector field behaves as a constant. Finally, slow-roll analysis is performed and slow-roll conditions are defined for this model, which, for suitable constraints of the model parameters, can give the required number of e-folds for sufficient inflation.

Constraining quantum collapse inflationary models with current data: The semiclassical approach

The hypothesis of the self-induced collapse of the inflaton wave function was introduced as a candidate for the physical process responsible for the emergence of inhomogeneity and anisotropy at all scales. In particular, we consider different proposal for the precise form of the dynamics of the inflaton wave function: (i) the GRW-type collapse schemes proposals based on spontaneous individual collapses which generate nonvanishing expectation values of various physical quantities taken as ansatz modifications of the standard inflationary scenario; (ii) the proposal based on a Continuous Spontaneous Localization (CSL) type modification of the Schrödinger evolution of the inflaton wave function, based on a natural choice of collapse operator. We perform a systematic analysis within the semi-classical gravity approximation, of the standing of those models considering a full quasi-de Sitter expansion scenario. We note that the predictions for the Cosmic Microwave Background (CMB) temperature and polarization spectrum differ slightly from those of the standard cosmological model. We also analyze these proposals with a Bayesian model comparison using recent CMB and Baryonic Acoustic Oscillations (BAO) data. Our results show a moderate preference of the joint CMB and BAO data for one of the studied collapse schemes model over the [Formula: see text]CDM one, while there is no preference when only CMB data are considered. Additionally, analysis using CMB data provide the same Bayesian evidence for both the CSL and Standard Models, i.e. the data have no preference between the simplicity of the LCDM model and the complexity of the collapse scenario.

Reconstruction method of f(R) gravity for isotropic and anisotropic spacetimes

We present the reconstruction method of $f(R)$ gravity for the homogeneous and anisotropic Bianchi-I spacetime, which was previously formulated only for homogeneous and isotropic FLRW spacetime. We argue in this paper that for anisotropic spacetimes, the total anisotropy behaves as an independent metric degree of freedom on top of the average scale factor in $f(R)$ gravity. This is not like $GR$, where specifying the form of the average scale factor as a function of time also specify the total anisotropy as a function of time uniqely. We link this peculiar fact to an interesting intertwining between the definition of Ricci scalar for anisotropic metric and anisotropy evolution equation in $f(R)$ gravity. Consequently, specifying an anisotropic solution of $f(R)$ gravity implies specifying both the average scale factor and the total anisotropy as functions of time. The reconstruction method hence formulated is applied to two scenarios where anisotropy suppression is important, namely, a quasi de-Sitter expansion as required in inflation, and a power law contraction as required in ekpyrotic bounce models.

Dark matter and baryon asymmetry from the very dawn of the Universe

We propose a universal mechanism of producing dark matter and baryon (lepton) charge at the stage of the quasi-de Sitter expansion of the Universe---inflation. The key ingredient of the mechanism is a linear coupling of the field, responsible for generation of dark matter or baryon (lepton) charge, to a function of the inflaton. During inflation this induces almost constant force dragging the corresponding field to the non-zero value. This force explicitly breaks quantum numbers associated with dark matter/baryon abundance at later stages. As a particular realization of the mechanism we introduce a super-heavy complex scalar field with the mass larger than the Hubble rate during the last e-folds of inflation. The global U(1)-symmetry is violated due to the linear coupling of the phase of the complex scalar to the inflaton. The symmetry breaking leads to the generation of a non-zero Noether charge. The latter is directly related to the dark matter abundance, or, alternatively, can be converted into baryon asymmetry, if the complex scalar carries the baryon charge.

Study of some chaotic inflationary models in f ( R ) $f(R)$ gravity

In this paper, we discuss inflationary scenario via scalar field and fluid cosmology for anisotropic homogeneous universe model in $f(R)$ gravity. We consider an equation of state which corresponds to quasi-de Sitter expansion and investigate the effect of anisotropy parameter for different values of deviation parameter. We evaluate potential models like linear, quadratic and quartic which correspond to chaotic inflation. We construct the observational parameters for power-law model of $f(R)$ gravity and construct the graphical analysis of tensor-scalar ratio and spectral index which indicates consistency of these parameters with Planck 2015 data.

Inflationary dynamics in f(𝒢) gravity

This paper investigates inflationary dynamics for isotropic and homogeneous universe model in the background of [Formula: see text] gravity. We construct Hubble-flow functions, slow-roll parameters, amplitude of scalar power spectrum, spectral index and tensor–scalar ratio for a particular form of equation of state which describes quasi-de Sitter expansion. The dynamics of inflationary epoch is analyzed for scalar field as well as fluid cosmology with viable power-law [Formula: see text] model. We obtain different potential functions that correspond to chaotic inflation and Starobinsky type models. The graphical behavior of these parameters shows compatible results with observational Planck 2015 data in this gravity.

Slow-roll inflation from massive vector fields non-minimally coupled to gravity

In this work we study slow-roll inflation for a vector-tensor model with massive vector fields non-minimally coupled to gravity. The model under consideration has arbitrary parameters for each geometrical coupling. Taking into account a spatially flat FRW type universe and a general vector fields (with temporal and spatial components), we get the general expressions for equation of motion and the total energy momentum tensor. In this scenario, the isotropy of expansion is guaranteed considering a triplet of orthogonal vector fields, but the effective mass of the vector field is of the order of the Hubble scale and the inflationary regime is difficult to realize with this model. However, for suitable values (or constraints) of model parameters, it is possible to overcome this issue. In this sense, two cases were analyzed. In the first case, a regime with slow-roll inflation was obtained, and for the second case the vector field behaves as a constant, and it drives a quasi de Sitter expansion, hence that slow-roll takes place and inflation occurs.

Constraining quantum collapse inflationary models with CMB data

The hypothesis of the self-induced collapse of the inflaton wave function was proposed as responsible for the emergence of inhomogeneity and anisotropy at all scales. This proposal was studied within an almost de Sitter space-time approximation for the background, which led to a perfect scale-invariant power spectrum, and also for a quasi-de Sitter background, which allows to distinguish departures from the standard approach due to the inclusion of the collapse hypothesis. In this work we perform a Bayesian model comparison for two different choices of the self-induced collapse in a full quasi-de Sitter expansion scenario. In particular, we analyze the possibility of detecting the imprint of these collapse schemes at low multipoles of the anisotropy temperature power spectrum of the Cosmic Microwave Background (CMB) using the most recent data provided by the Planck Collaboration. Our results show that one of the two collapse schemes analyzed provides the same Bayesian evidence of the minimal standard cosmological model ΛCDM, while the other scenario is weakly disfavoured with respect to the standard cosmology.

Inflation including collapse of the wave function: the quasi-de Sitter case

The precise physical mechanism describing the emergence of the seeds of cosmic structure from a perfect isotropic and homogeneous universe has not been fully explained by the standard version of inflationary models. To handle this shortcoming, D. Sudarsky and collaborators have developed a proposal: the self-induced collapse hypothesis. In this scheme, the objective collapse of the inflaton wave function is responsible for the emergence of inhomogeneity and anisotropy at all scales. In previous papers, the proposal was developed with an almost exact de Sitter space-time approximation for the background that led to a perfect scale-invariant power spectrum. In the present article, we consider a full quasi-de Sitter expansion and calculate the primordial power spectrum for three different choices of the self-induced collapse. The consideration of a quasi-de Sitter background allows us to distinguish departures from an exact scale-invariant power spectrum that are due to the inclusion of the collapse hypothesis. These deviations are also different from the prediction of standard inflationary models with a running spectral index. A comparison with the primordial power spectrum and the CMB temperature fluctuation spectrum preferred by the latest observational data is also discussed. From the analysis performed in this work, it follows that most of the collapse schemes analyzed in this paper are viable candidates to explain the present observations of the CMB fluctuation spectrum.

Cosmological perturbations from stochastic gravity

In inflationary cosmological models driven by an inflaton field the origin of the primordial inhomogeneities which are responsible for large-scale structure formation are the quantum fluctuations of the inflaton field. These are usually calculated using the standard theory of cosmological perturbations, where both the gravitational and the inflaton fields are linearly perturbed and quantized. The correlation functions for the primordial metric fluctuations and their power spectrum are then computed. Here we introduce an alternative procedure for calculating the metric correlations based on the Einstein-Langevin equation which emerges in the framework of stochastic semiclassical gravity. We show that the correlation functions for the metric perturbations that follow from the Einstein-Langevin formalism coincide with those obtained with the usual quantization procedures when the scalar field perturbations are linearized. This method is explicitly applied to a simple model of chaotic inflation consisting of a Robertson-Walker background, which undergoes a quasi-de Sitter expansion, minimally coupled to a free massive quantum scalar field. The technique based on the Einstein-Langevin equation can, however, deal naturally with the perturbations of the scalar field even beyond the linear approximation, as is actually required in inflationary models which are not driven by an inflaton field, such as Starobinsky's trace-anomaly driven inflation or when calculating corrections due to nonlinear quantum effects in the usual inflaton driven models.

Gravitational waves from inflation on the brane

We discuss the evolution of gravitational waves in a brane-world cosmology embedded in five-dimensional anti-de Sitter spacetime. We show that during slow-roll inflation, modelled as a period of quasi-de Sitter expansion on the brane, there is a discrete normalizable massless graviton mode. There is a mass gap due to the expansion, above which there is a continuum of massive modes. Only the massless mode is `light' compared with the Hubble scale during inflation, leading to the production of classical perturbations on large scales from vacuum fluctuations on small scales. We calculate the amplitude of these fluctuations at horizon-crossing and show that the standard four-dimensional result is recovered at low energies, but the amplitude of the perturbations is enhanced at high energies.